Mechanical properties by raw material
ggplot(combined, aes(Raw.Material, ymodule)) + geom_point(aes(color=Raw.Material)) + ylab("Young's Modulus") + xlab("Raw Material") + ggtitle("Young's Modulus")

ggplot(combined, aes(Raw.Material, Leeb.Hardness)) + geom_point(aes(color=Raw.Material)) + xlab("Raw Material") + ylab("Leeb Harndess") + ggtitle("Leeb's Hardness") + theme(legend.title = element_text(colour="blue", size=15, face="bold"),legend.text = element_text(colour="red", size = 10, face = "bold"))

Subset by raw material
granite<-subset(combined, combined$Raw.Material=="granite")
rhyolite<-subset(combined, combined$Raw.Material=="rhyolite")
dacite<-subset(combined, combined$Raw.Material=="dacite")
fenitized_gneiss<-subset(combined, combined$Raw.Material=="fenitized gneiss")
carbonatite<-subset(combined, combined$Raw.Material=="carbonatite")
quartzite<-subset(combined, combined$Raw.Material=="quartzite")
Is there a relationship between crystallinity and raw material?
ggplot(combined, aes(Raw.Material, Percent.Area)) + geom_boxplot(aes(fill=Raw.Material)) + ylab("Percent Crystal") + xlab("Raw Material") + ggtitle("Crystallinity by Raw Material") + scale_fill_discrete(name="Raw Material") + theme(legend.title = element_text(colour="blue", size=15, face="bold"),legend.text = element_text(colour="red", size = 10, face = "bold"))

Angle and raw material?
ggplot(combined, aes(Raw.Material, Angle)) + geom_boxplot(aes(fill=Raw.Material)) + ylab("Angle") + xlab("Raw Material") + ggtitle("Crystal Angularity by Raw Material") + scale_fill_discrete(name="Raw Material") + theme(legend.title = element_text(colour="blue", size=15, face="bold"),legend.text = element_text(colour="red", size = 10, face = "bold"))

Crystal size and raw material?
ggplot(combined, aes(Raw.Material, Average.Size)) + geom_boxplot(aes(fill=Raw.Material)) + ylab("Average size") + xlab("Raw Material") + ggtitle("Average crystal size by Raw Material") + scale_fill_discrete(name="Raw Material") + theme(legend.title = element_text(colour="blue", size=15, face="bold"),legend.text = element_text(colour="red", size = 10, face = "bold"))
###Total area and raw material
ggplot(combined, aes(Raw.Material, Total.Area)) + geom_boxplot(aes(fill=Raw.Material)) + ylab("Total Area") + xlab("Raw Material") + ggtitle("Total Area by Raw Material") + scale_fill_discrete(name="Raw Material") + theme(legend.title = element_text(colour="blue", size=15, face="bold"),legend.text = element_text(colour="red", size = 10, face = "bold"))

Normality tests
Granite
shapiro.test(granite$Percent.Area)
##
## Shapiro-Wilk normality test
##
## data: granite$Percent.Area
## W = 0.99233, p-value = 0.2049
hist(granite$Percent.Area)

shapiro.test(granite$Angle)
##
## Shapiro-Wilk normality test
##
## data: granite$Angle
## W = 0.98835, p-value = 0.03605
hist(granite$Angle)

shapiro.test(granite$Average.Size)
##
## Shapiro-Wilk normality test
##
## data: granite$Average.Size
## W = 0.8806, p-value = 2.575e-13
hist(granite$Average.Size)

shapiro.test(granite$Total.Area)
##
## Shapiro-Wilk normality test
##
## data: granite$Total.Area
## W = 0.99234, p-value = 0.205
hist(granite$Total.Area)

Average crystal size for granite is not normally distributed which makes sense because granite tends to have a lot of smaller crystals and less larger crystals.
Rhyolite
shapiro.test(rhyolite$Percent.Area)
##
## Shapiro-Wilk normality test
##
## data: rhyolite$Percent.Area
## W = 0.88706, p-value < 2.2e-16
hist(rhyolite$Percent.Area)

shapiro.test(rhyolite$Angle)
##
## Shapiro-Wilk normality test
##
## data: rhyolite$Angle
## W = 0.99103, p-value = 0.0157
hist(rhyolite$Angle)

shapiro.test(rhyolite$Average.Size)
##
## Shapiro-Wilk normality test
##
## data: rhyolite$Average.Size
## W = 0.47961, p-value < 2.2e-16
hist(rhyolite$Average.Size)

shapiro.test(rhyolite$Total.Area)
##
## Shapiro-Wilk normality test
##
## data: rhyolite$Total.Area
## W = 0.88707, p-value < 2.2e-16
hist(rhyolite$Total.Area)

Carbonatite
shapiro.test(carbonatite$Percent.Area)
##
## Shapiro-Wilk normality test
##
## data: carbonatite$Percent.Area
## W = 0.98409, p-value = 0.005778
hist(carbonatite$Percent.Area)

shapiro.test(carbonatite$Angle)
##
## Shapiro-Wilk normality test
##
## data: carbonatite$Angle
## W = 0.99641, p-value = 0.8267
hist(carbonatite$Angle)

shapiro.test(carbonatite$Average.Size)
##
## Shapiro-Wilk normality test
##
## data: carbonatite$Average.Size
## W = 0.65585, p-value < 2.2e-16
hist(carbonatite$Average.Size)

shapiro.test(carbonatite$Total.Area)
##
## Shapiro-Wilk normality test
##
## data: carbonatite$Total.Area
## W = 0.98409, p-value = 0.005775
hist(carbonatite$Total.Area)

Dacite
shapiro.test(dacite$Percent.Area)
##
## Shapiro-Wilk normality test
##
## data: dacite$Percent.Area
## W = 0.96764, p-value = 3.153e-07
hist(dacite$Percent.Area)

shapiro.test(dacite$Angle)
##
## Shapiro-Wilk normality test
##
## data: dacite$Angle
## W = 0.97416, p-value = 4.336e-06
hist(dacite$Angle)

shapiro.test(dacite$Average.Size)
##
## Shapiro-Wilk normality test
##
## data: dacite$Average.Size
## W = 0.5693, p-value < 2.2e-16
hist(dacite$Average.Size)

shapiro.test(dacite$Total.Area)
##
## Shapiro-Wilk normality test
##
## data: dacite$Total.Area
## W = 0.96764, p-value = 3.152e-07
hist(dacite$Total.Area)

Quartzite
shapiro.test(quartzite$Percent.Area)
##
## Shapiro-Wilk normality test
##
## data: quartzite$Percent.Area
## W = 0.98274, p-value = 2.76e-05
hist(quartzite$Percent.Area)

shapiro.test(quartzite$Angle)
##
## Shapiro-Wilk normality test
##
## data: quartzite$Angle
## W = 0.99184, p-value = 0.01259
hist(quartzite$Angle)

shapiro.test(quartzite$Average.Size)
##
## Shapiro-Wilk normality test
##
## data: quartzite$Average.Size
## W = 0.72762, p-value < 2.2e-16
hist(quartzite$Average.Size)

shapiro.test(quartzite$Total.Area)
##
## Shapiro-Wilk normality test
##
## data: quartzite$Total.Area
## W = 0.98274, p-value = 2.76e-05
hist(quartzite$Total.Area)

Fenitized gneiss
shapiro.test(fenitized_gneiss$Percent.Area)
##
## Shapiro-Wilk normality test
##
## data: fenitized_gneiss$Percent.Area
## W = 0.97922, p-value = 0.001074
hist(fenitized_gneiss$Percent.Area)

shapiro.test(fenitized_gneiss$Angle)
##
## Shapiro-Wilk normality test
##
## data: fenitized_gneiss$Angle
## W = 0.88965, p-value = 1.798e-12
hist(fenitized_gneiss$Angle)

shapiro.test(fenitized_gneiss$Average.Size)
##
## Shapiro-Wilk normality test
##
## data: fenitized_gneiss$Average.Size
## W = 0.7299, p-value < 2.2e-16
hist(fenitized_gneiss$Average.Size)

shapiro.test(fenitized_gneiss$Total.Area)
##
## Shapiro-Wilk normality test
##
## data: fenitized_gneiss$Total.Area
## W = 0.97922, p-value = 0.001075
hist(fenitized_gneiss$Total.Area)

Non-Parametric ANOVA
kruskal.test(Percent.Area ~ Raw.Material , data=combined)
##
## Kruskal-Wallis rank sum test
##
## data: Percent.Area by Raw.Material
## Kruskal-Wallis chi-squared = 1072.6, df = 5, p-value < 2.2e-16
kruskal.test(Average.Size ~ Raw.Material , data=combined)
##
## Kruskal-Wallis rank sum test
##
## data: Average.Size by Raw.Material
## Kruskal-Wallis chi-squared = 1166.6, df = 5, p-value < 2.2e-16
crystalinity is significantly different by raw material Average size is significantly different by raw material
ANOVA ANALYSIS
leeb hardness ~ rawmaterial * Percent.crystals
Leeb_PA<-lm(combined$Leeb.Hardness ~ combined$Raw.Material * combined$Percent.Area)
Leeb_PA
##
## Call:
## lm(formula = combined$Leeb.Hardness ~ combined$Raw.Material *
## combined$Percent.Area)
##
## Coefficients:
## (Intercept)
## 2.848e+02
## combined$Raw.Materialdacite
## -6.153e+01
## combined$Raw.Materialfenitized gneiss
## -7.376e+01
## combined$Raw.Materialgranite
## -1.216e+02
## combined$Raw.Materialquartzite
## -1.058e+02
## combined$Raw.Materialrhyolite
## -1.008e+02
## combined$Percent.Area
## -8.024e-14
## combined$Raw.Materialdacite:combined$Percent.Area
## 8.024e-14
## combined$Raw.Materialfenitized gneiss:combined$Percent.Area
## 8.024e-14
## combined$Raw.Materialgranite:combined$Percent.Area
## 8.024e-14
## combined$Raw.Materialquartzite:combined$Percent.Area
## 8.024e-14
## combined$Raw.Materialrhyolite:combined$Percent.Area
## 8.024e-14
pander(anova(Leeb_PA))
## Warning in anova.lm(Leeb_PA): ANOVA F-tests on an essentially perfect fit
## are unreliable
Analysis of Variance Table (continued below)
| combined$Raw.Material |
5 |
2701732 |
540346 |
| combined$Percent.Area |
1 |
4.757e-23 |
4.757e-23 |
| combined\(Raw.Material:combined\)Percent.Area |
5 |
1.367e-22 |
2.735e-23 |
| Residuals |
1974 |
1.438e-19 |
7.284e-23 |
| combined$Raw.Material |
7.418e+27 |
0 |
| combined$Percent.Area |
0.653 |
0.4191 |
| combined\(Raw.Material:combined\)Percent.Area |
0.3755 |
0.8658 |
| Residuals |
NA |
NA |
Leeb_PA_plot<-ggplot(combined, aes(y=Percent.Area , x=Leeb.Hardness , fill=Raw.Material)) + geom_boxplot() + ylab("Percent Area") + xlab("Leeb Hardness") + ggtitle("Leeb hardness by Raw material with Percent Crystal")
Leeb_PA_plot

leeb hardness ~ rawmaterial * total area
Leeb_TotalA<-lm(combined$Leeb.Hardness ~ combined$Raw.Material *combined$Total.Area)
Leeb_TotalA
##
## Call:
## lm(formula = combined$Leeb.Hardness ~ combined$Raw.Material *
## combined$Total.Area)
##
## Coefficients:
## (Intercept)
## 2.848e+02
## combined$Raw.Materialdacite
## -6.153e+01
## combined$Raw.Materialfenitized gneiss
## -7.376e+01
## combined$Raw.Materialgranite
## -1.216e+02
## combined$Raw.Materialquartzite
## -1.058e+02
## combined$Raw.Materialrhyolite
## -1.008e+02
## combined$Total.Area
## -1.087e-13
## combined$Raw.Materialdacite:combined$Total.Area
## 1.087e-13
## combined$Raw.Materialfenitized gneiss:combined$Total.Area
## 1.087e-13
## combined$Raw.Materialgranite:combined$Total.Area
## 1.087e-13
## combined$Raw.Materialquartzite:combined$Total.Area
## 1.087e-13
## combined$Raw.Materialrhyolite:combined$Total.Area
## 1.087e-13
pander(anova(Leeb_TotalA))
## Warning in anova.lm(Leeb_TotalA): ANOVA F-tests on an essentially perfect
## fit are unreliable
Analysis of Variance Table (continued below)
| combined$Raw.Material |
5 |
2701732 |
540346 |
| combined$Total.Area |
1 |
4.758e-23 |
4.758e-23 |
| combined\(Raw.Material:combined\)Total.Area |
5 |
1.368e-22 |
2.735e-23 |
| Residuals |
1974 |
1.438e-19 |
7.284e-23 |
| combined$Raw.Material |
7.418e+27 |
0 |
| combined$Total.Area |
0.6531 |
0.4191 |
| combined\(Raw.Material:combined\)Total.Area |
0.3755 |
0.8657 |
| Residuals |
NA |
NA |
Leeb_TotalA_plot<-ggplot(combined, aes(y=Total.Area , x=Leeb.Hardness , fill=Raw.Material)) + geom_boxplot() + ylab("Total Area") + xlab("Leeb Hardness") + ggtitle("Leeb hardness by Raw material with Total Area")
Leeb_TotalA_plot

leeb hardness ~ rawmaterial * average size
Leeb_AveSize<-lm(combined$Leeb.Hardness ~ combined$Raw.Material *combined$Average.Size)
Leeb_AveSize
##
## Call:
## lm(formula = combined$Leeb.Hardness ~ combined$Raw.Material *
## combined$Average.Size)
##
## Coefficients:
## (Intercept)
## 2.848e+02
## combined$Raw.Materialdacite
## -6.153e+01
## combined$Raw.Materialfenitized gneiss
## -7.376e+01
## combined$Raw.Materialgranite
## -1.216e+02
## combined$Raw.Materialquartzite
## -1.058e+02
## combined$Raw.Materialrhyolite
## -1.008e+02
## combined$Average.Size
## -9.128e-12
## combined$Raw.Materialdacite:combined$Average.Size
## 9.128e-12
## combined$Raw.Materialfenitized gneiss:combined$Average.Size
## 9.128e-12
## combined$Raw.Materialgranite:combined$Average.Size
## 9.128e-12
## combined$Raw.Materialquartzite:combined$Average.Size
## 9.128e-12
## combined$Raw.Materialrhyolite:combined$Average.Size
## 9.128e-12
pander(anova(Leeb_AveSize))
## Warning in anova.lm(Leeb_AveSize): ANOVA F-tests on an essentially perfect
## fit are unreliable
Analysis of Variance Table (continued below)
| combined$Raw.Material |
5 |
2701732 |
540346 |
| combined$Average.Size |
1 |
7.511e-23 |
7.511e-23 |
| combined\(Raw.Material:combined\)Average.Size |
5 |
6.473e-23 |
1.295e-23 |
| Residuals |
1974 |
1.438e-19 |
7.287e-23 |
| combined$Raw.Material |
7.416e+27 |
0 |
| combined$Average.Size |
1.031 |
0.3101 |
| combined\(Raw.Material:combined\)Average.Size |
0.1777 |
0.971 |
| Residuals |
NA |
NA |
Leeb_AveSize_plot<-ggplot(combined, aes(y=Average.Size , x=Leeb.Hardness , fill=Raw.Material)) + geom_boxplot() + ylab("Average Size") + xlab("Leeb Hardness") + ggtitle("Leeb hardness by Raw material with Average Size")
Leeb_AveSize_plot

leeb hardness ~ raw material * Angle
Leeb_Angle<-lm(combined$Leeb.Hardness ~ combined$Raw.Material *combined$Angle)
Leeb_Angle
##
## Call:
## lm(formula = combined$Leeb.Hardness ~ combined$Raw.Material *
## combined$Angle)
##
## Coefficients:
## (Intercept)
## 2.848e+02
## combined$Raw.Materialdacite
## -6.153e+01
## combined$Raw.Materialfenitized gneiss
## -7.376e+01
## combined$Raw.Materialgranite
## -1.216e+02
## combined$Raw.Materialquartzite
## -1.058e+02
## combined$Raw.Materialrhyolite
## -1.008e+02
## combined$Angle
## 1.159e-13
## combined$Raw.Materialdacite:combined$Angle
## -1.159e-13
## combined$Raw.Materialfenitized gneiss:combined$Angle
## -1.159e-13
## combined$Raw.Materialgranite:combined$Angle
## -1.159e-13
## combined$Raw.Materialquartzite:combined$Angle
## -1.159e-13
## combined$Raw.Materialrhyolite:combined$Angle
## -1.159e-13
pander(anova(Leeb_Angle))
## Warning in anova.lm(Leeb_Angle): ANOVA F-tests on an essentially perfect
## fit are unreliable
Analysis of Variance Table (continued below)
| combined$Raw.Material |
5 |
2701732 |
540346 |
7.41e+27 |
| combined$Angle |
1 |
3.356e-24 |
3.356e-24 |
0.04602 |
| combined\(Raw.Material:combined\)Angle |
5 |
2.444e-23 |
4.887e-24 |
0.06702 |
| Residuals |
1974 |
1.439e-19 |
7.292e-23 |
NA |
| combined$Raw.Material |
0 |
| combined$Angle |
0.8302 |
| combined\(Raw.Material:combined\)Angle |
0.9969 |
| Residuals |
NA |
Leeb_Angle_plot<-ggplot(combined, aes(y=Angle , x=Leeb.Hardness , fill=Raw.Material)) + geom_boxplot() + ylab("Angularity") + xlab("Leeb Hardness") + ggtitle("Leeb hardness by Raw material with Angularity")
Leeb_Angle_plot

youngsm ~ raw material * Percent.crystals
youngs_PA<-lm(combined$ymodule ~ combined$Raw.Material * combined$Percent.Area)
youngs_PA
##
## Call:
## lm(formula = combined$ymodule ~ combined$Raw.Material * combined$Percent.Area)
##
## Coefficients:
## (Intercept)
## 3.830e+00
## combined$Raw.Materialdacite
## 2.230e+00
## combined$Raw.Materialfenitized gneiss
## 1.770e+00
## combined$Raw.Materialgranite
## 6.200e-01
## combined$Raw.Materialquartzite
## 1.640e+00
## combined$Raw.Materialrhyolite
## 7.030e+00
## combined$Percent.Area
## 1.646e-15
## combined$Raw.Materialdacite:combined$Percent.Area
## -1.646e-15
## combined$Raw.Materialfenitized gneiss:combined$Percent.Area
## -1.646e-15
## combined$Raw.Materialgranite:combined$Percent.Area
## -1.646e-15
## combined$Raw.Materialquartzite:combined$Percent.Area
## -1.646e-15
## combined$Raw.Materialrhyolite:combined$Percent.Area
## -1.646e-15
pander(anova(youngs_PA))
## Warning in anova.lm(youngs_PA): ANOVA F-tests on an essentially perfect fit
## are unreliable
Analysis of Variance Table (continued below)
| combined$Raw.Material |
5 |
11222 |
2244 |
| combined$Percent.Area |
1 |
2.001e-26 |
2.001e-26 |
| combined\(Raw.Material:combined\)Percent.Area |
5 |
5.752e-26 |
1.15e-26 |
| Residuals |
1974 |
3.243e-23 |
1.643e-26 |
| combined$Raw.Material |
1.366e+29 |
0 |
| combined$Percent.Area |
1.218 |
0.2699 |
| combined\(Raw.Material:combined\)Percent.Area |
0.7003 |
0.6233 |
| Residuals |
NA |
NA |
youngs_PA_plot<-ggplot(combined, aes(y=Percent.Area , x=ymodule , fill=Raw.Material)) + geom_boxplot() + ylab("Percent Area") + xlab("Young's Modulas") + ggtitle("Young's modulas by Raw material with Percent Crystal")
youngs_PA_plot

youngsm ~ raw material * total area
youngs_TotalA<-lm(combined$ymodule ~ combined$Raw.Material *combined$Total.Area)
youngs_TotalA
##
## Call:
## lm(formula = combined$ymodule ~ combined$Raw.Material * combined$Total.Area)
##
## Coefficients:
## (Intercept)
## 3.830e+00
## combined$Raw.Materialdacite
## 2.230e+00
## combined$Raw.Materialfenitized gneiss
## 1.770e+00
## combined$Raw.Materialgranite
## 6.200e-01
## combined$Raw.Materialquartzite
## 1.640e+00
## combined$Raw.Materialrhyolite
## 7.030e+00
## combined$Total.Area
## 2.229e-15
## combined$Raw.Materialdacite:combined$Total.Area
## -2.229e-15
## combined$Raw.Materialfenitized gneiss:combined$Total.Area
## -2.229e-15
## combined$Raw.Materialgranite:combined$Total.Area
## -2.229e-15
## combined$Raw.Materialquartzite:combined$Total.Area
## -2.229e-15
## combined$Raw.Materialrhyolite:combined$Total.Area
## -2.229e-15
pander(anova(youngs_TotalA))
## Warning in anova.lm(youngs_TotalA): ANOVA F-tests on an essentially perfect
## fit are unreliable
Analysis of Variance Table (continued below)
| combined$Raw.Material |
5 |
11222 |
2244 |
| combined$Total.Area |
1 |
2.001e-26 |
2.001e-26 |
| combined\(Raw.Material:combined\)Total.Area |
5 |
5.753e-26 |
1.151e-26 |
| Residuals |
1974 |
3.243e-23 |
1.643e-26 |
| combined$Raw.Material |
1.366e+29 |
0 |
| combined$Total.Area |
1.218 |
0.2699 |
| combined\(Raw.Material:combined\)Total.Area |
0.7004 |
0.6232 |
| Residuals |
NA |
NA |
youngs_TotalA_plot<-ggplot(combined, aes(y=Total.Area , x=ymodule , fill=Raw.Material)) + geom_boxplot() + ylab("Total Area") + xlab("Young's Modulas") + ggtitle("Young's modulas by Raw material with Total Area")
youngs_TotalA_plot

youngsm ~ raw material * average size
youngs_AveSize<-lm(combined$ymodule ~ combined$Raw.Material *combined$Average.Size)
youngs_AveSize
##
## Call:
## lm(formula = combined$ymodule ~ combined$Raw.Material * combined$Average.Size)
##
## Coefficients:
## (Intercept)
## 3.830e+00
## combined$Raw.Materialdacite
## 2.230e+00
## combined$Raw.Materialfenitized gneiss
## 1.770e+00
## combined$Raw.Materialgranite
## 6.200e-01
## combined$Raw.Materialquartzite
## 1.640e+00
## combined$Raw.Materialrhyolite
## 7.030e+00
## combined$Average.Size
## 1.234e-13
## combined$Raw.Materialdacite:combined$Average.Size
## -1.234e-13
## combined$Raw.Materialfenitized gneiss:combined$Average.Size
## -1.234e-13
## combined$Raw.Materialgranite:combined$Average.Size
## -1.234e-13
## combined$Raw.Materialquartzite:combined$Average.Size
## -1.234e-13
## combined$Raw.Materialrhyolite:combined$Average.Size
## -1.234e-13
pander(anova(youngs_AveSize))
## Warning in anova.lm(youngs_AveSize): ANOVA F-tests on an essentially
## perfect fit are unreliable
Analysis of Variance Table (continued below)
| combined$Raw.Material |
5 |
11222 |
2244 |
| combined$Average.Size |
1 |
1.373e-26 |
1.373e-26 |
| combined\(Raw.Material:combined\)Average.Size |
5 |
1.183e-26 |
2.367e-27 |
| Residuals |
1974 |
3.248e-23 |
1.646e-26 |
| combined$Raw.Material |
1.364e+29 |
0 |
| combined$Average.Size |
0.8345 |
0.3611 |
| combined\(Raw.Material:combined\)Average.Size |
0.1438 |
0.9819 |
| Residuals |
NA |
NA |
youngs_AveSize_plot<-ggplot(combined, aes(y=Average.Size , x=Leeb.Hardness , fill=Raw.Material)) + geom_boxplot() + ylab("Average Size") + xlab("Young's Modulas") + ggtitle("Young's modulas by Raw material with Average Size")
youngs_AveSize_plot

youngs ~ raw material * Angle
youngs_Angle<-lm(combined$ymodule ~ combined$Raw.Material *combined$Angle)
youngs_Angle
##
## Call:
## lm(formula = combined$ymodule ~ combined$Raw.Material * combined$Angle)
##
## Coefficients:
## (Intercept)
## 3.830e+00
## combined$Raw.Materialdacite
## 2.230e+00
## combined$Raw.Materialfenitized gneiss
## 1.770e+00
## combined$Raw.Materialgranite
## 6.200e-01
## combined$Raw.Materialquartzite
## 1.640e+00
## combined$Raw.Materialrhyolite
## 7.030e+00
## combined$Angle
## 1.041e-14
## combined$Raw.Materialdacite:combined$Angle
## -1.041e-14
## combined$Raw.Materialfenitized gneiss:combined$Angle
## -1.041e-14
## combined$Raw.Materialgranite:combined$Angle
## -1.041e-14
## combined$Raw.Materialquartzite:combined$Angle
## -1.041e-14
## combined$Raw.Materialrhyolite:combined$Angle
## -1.041e-14
pander(anova(youngs_Angle))
## Warning in anova.lm(youngs_Angle): ANOVA F-tests on an essentially perfect
## fit are unreliable
Analysis of Variance Table (continued below)
| combined$Raw.Material |
5 |
11222 |
2244 |
1.372e+29 |
| combined$Angle |
1 |
2.708e-26 |
2.708e-26 |
1.656 |
| combined\(Raw.Material:combined\)Angle |
5 |
1.972e-25 |
3.944e-26 |
2.411 |
| Residuals |
1974 |
3.228e-23 |
1.635e-26 |
NA |
| combined$Raw.Material |
0 |
| combined$Angle |
0.1983 |
| combined\(Raw.Material:combined\)Angle |
0.03438 |
| Residuals |
NA |
youngs_Angle_plot<-ggplot(combined, aes(y=Angle , x=ymodule , fill=Raw.Material)) + geom_boxplot() + ylab("Angularity") + xlab("Young's Modulas") + ggtitle("Young's modulas by Raw material with Angularity")
youngs_Angle_plot
